Feynman rules of quantum chromodynamics inside a hadron

Abstract

We start from quantum chromodynamics in a finite volume of linear size $L$ and examine its color-dielectric constant ${\kappa }_L$, especially the limit ${\kappa }_{\infty }$ as $L\to \infty$. By choosing as our standard ${\kappa }_L=1\mathrm{}$ when $L=\mathrm{some}\mathrm{hadron}\mathrm{size} R$, we conclude that ${\kappa }_{\infty }$ must be ${\kappa }_{\infty }<1.3\mathrm{}\times {10}^{-2\mathrm{}}\alpha$ where $\alpha$ is the fine-structure constant of QCD inside the hadron. A permanent quark confinement corresponds to the limit ${\kappa }_{\infty }=0\mathrm{}$. The hadrons are viewed as small domain structures (with color-dielectric constant = 1) immersed in a perfect, or nearly perfect, color-dia-electric medium, which is the vacuum. The Feynman rules of QCD inside the hadron are derived; they are found to depend on the color-dielectric constant ${\kappa }_{\infty }$ of the vacuum that lies outside. We show that, when ${\kappa }_{\infty }\to 0$, the mass of any color-nonsinglet state becomes $\infty$, but for color-singlet states their masses and scattering amplitudes remain finite. These new Feynman rules also depend on the hadron size $R$. Only at high energy and large four-momentum transfer can such $R$ dependence be neglected and, for color-singlet states, these new rules be reduced to the usual ones.